This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs). In this approach

a nonlinear two-point boundary value problem (TPBVP)

derived from Pontryagin’s maximum principle

is transformed into a sequence of linear time-invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series. Hence

to obtain the optimal solution

only the techniques for solving linear ordinary differential equations are employed. An efficient algorithm is also presented

which has low computational complexity and a fast convergence rate. Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP. The results not only demonstrate the efficiency

simplicity

and high accuracy of the suggested approach

but also indicate its effectiveness in practical use.